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A Numerical Computation for Inverse Boundary Determination Problem

By Y. C. Hon and Zongmin Wu


: Based on the idea of radial basis interpolation for HermiteBirkho data and the shift invariability of harmonic function space, a new computational method is developed to determine an unknown boundary of a domain from given values of the solution and its derivatives on only part of the other boundary. This is a well known inverse boundary determination problem which arises from using non-destructive evaluation technique in the engineering industry. Error estimation of the computational method is also given and the numerical results indicate that the method provides an accurate approximation of the unknown boundary. AMS classications: 65N, 35R Keywords: Radial Basis Interpolation, Harmonic Function, Inverse Boundary Determination. 1 1 Introduction Consider a bounded domain 2 < 2 with boundary @ Assume that an inaccessible part of the boundary has been damaged with, for example, corrosion. An inverse boundary determination problem is to determine the shape of the corroded par..

Topics: Radial Basis Interpolation, Harmonic Function, Inverse Boundary Determination. 1
Year: 2000
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